Chapter 5 A Closed-Economy One-Period Macroeconomic Model

Chapter 5 A Closed-Economy One-Period Macroeconomic Model 51
8. We need to analyze each case separately. Start with the good equilibrium. As government expenses
increase, more tax revenue needs to be raised, and thus the tax rate needs to be increased. As shown
in the figure below, this tilts down the linear PPF. The new equilibrium leads to a lower indifference
curve. This leads to a negative income effect and a lower wage (remember, it is z(1 − t)), thus a
substitution effect. The income effect lowers consumption and leisure, the substitution effect
decreases consumption and increases leisure. All in all, consumption is lower and leisure is higher, as
we know that the substitution effect dominates the income effect. This means that the labor supply is
reduced, and thus equilibrium labor and output.
The story is different in the bad equilibrium. To increase tax revenue, one needs to reduce the tax
rate. Then all the changes discussed above are exactly in the opposite direction.
9. We know from previous analysis that an improvement in total factor productivity pushes up the PPF,
and thus leads to an increase in consumption, a decrease in leisure, and thus an increase in the
quantity of labor supplied. This increases the tax base, and thus allows to reduce the tax rate to
achieve the same tax revenue, or in other words, it pushes the left portion of the Laffer curve to the
left. The reduction in the tax rate has then a further impact on the variables of interest: as we saw
in question 7, first part with a reversal of all signs: consumption increases even more and leisure
decrease yet more, leading to an even higher quantity of labor. All in all, as both labor and total factor
productivity increase, output increases.